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Since some years the gas electron multipliers (GEM)based detectors have been proposed for many different applications, in particular, in high-energy physics and astrophysics experiments and medical imaging. Many experimental measurements and tests have been performed to investigate their characteristics and performances. To achieve a better understanding of the behavior of this kind of detector the computer simulation is a very important tool. In this paper, a complete and detailed simulation of a triple-GEM-based detector is described. A method has been developed to take into account all the processes from the ionization mechanism up to the signal formation and electronic response. The results obtained are compared with experimental data and a very good agreement is achieved.